Ocean Currents in a Non-homogeneous Ocean 509 



particularly valuable since this is not the case of the individual constituents of the 

 "elementar" current. 



{a) Volume and Mass Transport 



If the action of the wind at the sea surface producing a drift current almost indepen- 

 dent on the mass structure is disregarded, then the "elementar" current according to 

 Ekman (see p.41 3) is made up of a pure gradient current and a density current. The gradi- 

 ent current depends only on the slope of the physical sea level and, if the bottom layer is 

 disregarded, represents a flow in geostrophic balance independent on the depth 

 (equation X.4), while the density current depends only on the distribution of mass in 

 the interior of the ocean. This mass distribution allows to evaluate the relative vertical 

 velocity distribution in the density current (equations XV.7 and 12). The total vertical 

 pressure distribution in the ocean equally is composed of two parts. The first one 

 originates from the slope of the physical sea level and is independent on the depth. 

 If the deviation of the sea level from its equilibrium position (level surface) is denoted 

 by ^ (positive upwards), then the resultant pressure disturbance will be Ap = gpt,. 

 The second part p, originates from the mass distribution in the interior of the sea so 

 that p = Pi-\- Ap. 



For a steady frictionless state the equations of motion will be 



u = --.i^-\-U and v= -. P + K, (XV.16) 



f dy f ox 



where U and V are the components of the geostrophic current (equation XIII.4). 

 The first term on the right-hand side in these equations gives the density current which 

 v\'ill have velocity components 



Introducing instead of pressure the dynamic depth of the isobaric surfaces D, accord- 

 ing to (IX. 8), and taking into consideration that the unit of the potential is —lOD 

 (equation IX.4), then one obtains from 



10 cD , 10 8D 



u, = -^ ^ and Vi = - -y -^ , (XV. 18) 



f dy ' f dx ' 



whereby D can also be replaced by the anomaly of the dynamic depth. The volume 

 transport in a horizontal flow is given by 



^x — 



u dz and 5„ = 



vdz (XV. 19) 



and the mass transport by the components 



M:, 



■d 



pu dz and My = 



rd 



pv dz, (XV.20) 



where d is the depth of the sea. The corresponding quantities for the pure gradient 

 current can be written down immediately since it is independent on the depth. The 



